Pub Date : 2023-07-01DOI: 10.46793/match.90-3.765a
S. Akbari, M. Habibi, Soheyr Rouhani
{"title":"A Note on an Inequality Between Energy and Sombor Index of a Graph","authors":"S. Akbari, M. Habibi, Soheyr Rouhani","doi":"10.46793/match.90-3.765a","DOIUrl":"https://doi.org/10.46793/match.90-3.765a","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"24 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84293737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.46793/match.90-3.787a
Mahsa Arabzadeh, G. Fath-Tabar, Hamid Rasoli, A. Tehranian
{"title":"Estrada and L-Estrada Indices of a Graph and Their Relationship with the Number of Spanning Trees","authors":"Mahsa Arabzadeh, G. Fath-Tabar, Hamid Rasoli, A. Tehranian","doi":"10.46793/match.90-3.787a","DOIUrl":"https://doi.org/10.46793/match.90-3.787a","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"1 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79731483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.46793/match.90-3.609x
Changjin Xu, Qing Cui, Zixin Liu, Yuanlu Pan, Xiaohan Cui, Wei-Bo Ou, Mati ur Rahman, Muhammad Farman, Shabir Ahmad, A. Zeb
Fractional-order differential models plays a pivotal role in depicting the relationship among concentration changes of various chemical substances in chemistry. In this current study, we will explore the dynamics of a delayed chemostat model. First of all, we prove that the solution of the delayed chemostat model exists and is unique by virtue of fixed point theorem. Secondly, we demonstrate that the solution of the delayed chemostat model is non-negative by applying some suitable inequality strategies. Thirdly, the boundedness of the solution to the delayed chemostat model is explored via constructing a reasonable function. Fourthly, the Hopf bifurcation and stability of the delayed chemostat model are dealt with by exploiting the stability criterion and bifurcation theory on fractional dynamical system. Fifthly, the stability domain and Hopf bifurcation of the delayed chemostat model are resoundingly controlled by making use of an extended hybrid controller. Sixthly, the stability domain and Hopf bifurcation of the delayed chemostat model are effectively adjusted by making use of an another extended hybrid controller. The role of delay in this chemostat model is revealed. Seventhly, software experiments are given to illustrate the rightness of the gained key conclusions. The acquired outcomes of this work are perfectly innovative and have crucial theoretical value in controlling the concentrations of various chemical substances.
{"title":"Extended Hybrid Controller Design of Bifurcation in a Delayed Chemostat Model","authors":"Changjin Xu, Qing Cui, Zixin Liu, Yuanlu Pan, Xiaohan Cui, Wei-Bo Ou, Mati ur Rahman, Muhammad Farman, Shabir Ahmad, A. Zeb","doi":"10.46793/match.90-3.609x","DOIUrl":"https://doi.org/10.46793/match.90-3.609x","url":null,"abstract":"Fractional-order differential models plays a pivotal role in depicting the relationship among concentration changes of various chemical substances in chemistry. In this current study, we will explore the dynamics of a delayed chemostat model. First of all, we prove that the solution of the delayed chemostat model exists and is unique by virtue of fixed point theorem. Secondly, we demonstrate that the solution of the delayed chemostat model is non-negative by applying some suitable inequality strategies. Thirdly, the boundedness of the solution to the delayed chemostat model is explored via constructing a reasonable function. Fourthly, the Hopf bifurcation and stability of the delayed chemostat model are dealt with by exploiting the stability criterion and bifurcation theory on fractional dynamical system. Fifthly, the stability domain and Hopf bifurcation of the delayed chemostat model are resoundingly controlled by making use of an extended hybrid controller. Sixthly, the stability domain and Hopf bifurcation of the delayed chemostat model are effectively adjusted by making use of an another extended hybrid controller. The role of delay in this chemostat model is revealed. Seventhly, software experiments are given to illustrate the rightness of the gained key conclusions. The acquired outcomes of this work are perfectly innovative and have crucial theoretical value in controlling the concentrations of various chemical substances.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"15 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87578371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.46793/match.90-3.649h
Jing Huang, Minjie Zhang
{"title":"On the Harary Index of Graphs with Given Dissociation Number","authors":"Jing Huang, Minjie Zhang","doi":"10.46793/match.90-3.649h","DOIUrl":"https://doi.org/10.46793/match.90-3.649h","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"46 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82310787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-01DOI: 10.46793/match.90-2.315p
H. Peker, Fatma Aybike Çuha, Bilge Peker
In most of the real life problems, we encounter with nonlinear differential equations. Problems are made more understandable by modeling them with these equations. In this way, it becomes easier to interpret the problems and reach the results. In 1913, the basic enzymatic reaction model introduced by Michaelis and Menten to describe enzyme processes is an example of nonlinear differential equation. This model is the one of the simplest and best-known approaches of the mechanisms used to model enzyme-catalyzed reactions and is the most studied. For most nonlinear differential equations, it is very difficult to get an analytical solution. For this reason, various studies have been carried out to find approximate solutions to such equations. Among these studies, those in which two different methods are used by blending attract attention. In this study, a blended form of the Kashuri Fundo transform method and the Adomian decomposition method, so-called the Kashuri Fundo decomposition method, is used to find a solution to the Michaelis-Menten nonlinear biochemical reaction model in this way. This method has been applied to the biochemical reaction model and an approximate solution has been obtained for this model without complex calculations. This shows that the hybrid method is an effective, reliable, simpler and time-saving method in reaching the solutions of nonlinear differential equations.
{"title":"Kashuri Fundo Decomposition Method for Solving Michaelis-Menten Nonlinear Biochemical Reaction Model","authors":"H. Peker, Fatma Aybike Çuha, Bilge Peker","doi":"10.46793/match.90-2.315p","DOIUrl":"https://doi.org/10.46793/match.90-2.315p","url":null,"abstract":"In most of the real life problems, we encounter with nonlinear differential equations. Problems are made more understandable by modeling them with these equations. In this way, it becomes easier to interpret the problems and reach the results. In 1913, the basic enzymatic reaction model introduced by Michaelis and Menten to describe enzyme processes is an example of nonlinear differential equation. This model is the one of the simplest and best-known approaches of the mechanisms used to model enzyme-catalyzed reactions and is the most studied. For most nonlinear differential equations, it is very difficult to get an analytical solution. For this reason, various studies have been carried out to find approximate solutions to such equations. Among these studies, those in which two different methods are used by blending attract attention. In this study, a blended form of the Kashuri Fundo transform method and the Adomian decomposition method, so-called the Kashuri Fundo decomposition method, is used to find a solution to the Michaelis-Menten nonlinear biochemical reaction model in this way. This method has been applied to the biochemical reaction model and an approximate solution has been obtained for this model without complex calculations. This shows that the hybrid method is an effective, reliable, simpler and time-saving method in reaching the solutions of nonlinear differential equations.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"84 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74466097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-01DOI: 10.46793/match.90-2.381a
Liang Ai, Jie Feng, Yu-Hua Yao
In this paper, we propose a new fast alignment-free method for protein sequence similarity and evolutionary analysis. First 20 natural amino acids are clustered into 6 groups based on their physicochemical properties, then a 12-dimensional vector is constructed based on the frequency and the average position of occurrence of amino acids in each reduced amino acid sequences. Finally, the Euclidean distance is used to measure the similarity and evolutionary distance between protein sequences. The test on three datasets shows that our method can cluster each protein sequence accurately, which illustrates the effective of our method.
{"title":"A Novel Fast Approach for Protein Classification and Evolutionary Analysis","authors":"Liang Ai, Jie Feng, Yu-Hua Yao","doi":"10.46793/match.90-2.381a","DOIUrl":"https://doi.org/10.46793/match.90-2.381a","url":null,"abstract":"In this paper, we propose a new fast alignment-free method for protein sequence similarity and evolutionary analysis. First 20 natural amino acids are clustered into 6 groups based on their physicochemical properties, then a 12-dimensional vector is constructed based on the frequency and the average position of occurrence of amino acids in each reduced amino acid sequences. Finally, the Euclidean distance is used to measure the similarity and evolutionary distance between protein sequences. The test on three datasets shows that our method can cluster each protein sequence accurately, which illustrates the effective of our method.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"56 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73934735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-01DOI: 10.46793/match.90-2.471i
B. Ibrahim, Stephan Peter
Various types of dynamical systems, such as ordinary differential equations (ODEs) or partial differential equations (PDEs), are widely applied not only in chemistry but also in many scientific disciplines to model the dynamics arising from interactions described by reactions between molecules, individuals, or species. This study provides an overview of how Chemical Organization Theory (COT) can be used to analyze such systems by identifying all potentially persistent species solely from the underlying reaction network, without the need for simulations or even knowledge of reaction constants or kinetic laws. Two minimalist examples with only three resp. four species are used to introduce all fundamental definitions including a new, naturally arising concept of persistence, and to illustrate the fore-mentioned technique without mathematical details such as proofs. Thereby, COT is shown to provide measures to analyze, compare, and construct very complex systems on an abstract level and thus to complement other powerful techniques for the analysis of complex systems such as deficiency, RAF theory, elementary modes, graph theory, Lyapunov functions, and bifurcation theory.
{"title":"Persistent Subspaces of Reaction-Based Dynamical Systems","authors":"B. Ibrahim, Stephan Peter","doi":"10.46793/match.90-2.471i","DOIUrl":"https://doi.org/10.46793/match.90-2.471i","url":null,"abstract":"Various types of dynamical systems, such as ordinary differential equations (ODEs) or partial differential equations (PDEs), are widely applied not only in chemistry but also in many scientific disciplines to model the dynamics arising from interactions described by reactions between molecules, individuals, or species. This study provides an overview of how Chemical Organization Theory (COT) can be used to analyze such systems by identifying all potentially persistent species solely from the underlying reaction network, without the need for simulations or even knowledge of reaction constants or kinetic laws. Two minimalist examples with only three resp. four species are used to introduce all fundamental definitions including a new, naturally arising concept of persistence, and to illustrate the fore-mentioned technique without mathematical details such as proofs. Thereby, COT is shown to provide measures to analyze, compare, and construct very complex systems on an abstract level and thus to complement other powerful techniques for the analysis of complex systems such as deficiency, RAF theory, elementary modes, graph theory, Lyapunov functions, and bifurcation theory.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"48 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82238236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-01DOI: 10.46793/match.90-2.495l
Hechao Liu, L. You, Yufei Huang
,
，
{"title":"Sombor Index of c-Cyclic Chemical Graphs","authors":"Hechao Liu, L. You, Yufei Huang","doi":"10.46793/match.90-2.495l","DOIUrl":"https://doi.org/10.46793/match.90-2.495l","url":null,"abstract":",","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"31 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82684269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-01DOI: 10.46793/match.90-2.357q
Zhaohui Qi, Yingqiang Ning, Yinmei Huang
Based on 3-ary Huffman coding algorithm, we propose a digital mapping method of protein sequence. Firstly, a 3-ary Huffman tree is defined by the frequency characteristic of 20 amino acids in given protein sequences. The 0-2 codes of 20 amino acids constructed by the 3-ary Huffman tree can convert long protein sequences into one-to-one 0-2 digital sequences. According to the frequency characteristic and the distribution information of 0-2 codes of 20 amino acids in the 0-2 digital sequences, we design the 40-dimensional vectors to characterize the protein sequences. Next, the proposed digital mapping method is used to perform three separate applications, similarity comparison of nine ND6 proteins, evolutionary trend analysis of the 2009 pandemic Human influenza A (H1N1) viruses from January 2020 to June 2022, and the evolution analysis of 95 coronavirus genes. The results illustrate the utility of the proposed method.
{"title":"Protein Sequence Comparison Method Based on 3-ary Huffman Coding","authors":"Zhaohui Qi, Yingqiang Ning, Yinmei Huang","doi":"10.46793/match.90-2.357q","DOIUrl":"https://doi.org/10.46793/match.90-2.357q","url":null,"abstract":"Based on 3-ary Huffman coding algorithm, we propose a digital mapping method of protein sequence. Firstly, a 3-ary Huffman tree is defined by the frequency characteristic of 20 amino acids in given protein sequences. The 0-2 codes of 20 amino acids constructed by the 3-ary Huffman tree can convert long protein sequences into one-to-one 0-2 digital sequences. According to the frequency characteristic and the distribution information of 0-2 codes of 20 amino acids in the 0-2 digital sequences, we design the 40-dimensional vectors to characterize the protein sequences. Next, the proposed digital mapping method is used to perform three separate applications, similarity comparison of nine ND6 proteins, evolutionary trend analysis of the 2009 pandemic Human influenza A (H1N1) viruses from January 2020 to June 2022, and the evolution analysis of 95 coronavirus genes. The results illustrate the utility of the proposed method.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"1 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83045307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-01DOI: 10.46793/match.90-2.453b
S. Brezovnik, Niko Tratnik, Petra Žigert Pleteršek
The aim of this paper is to investigate resonance graphs of 2- connected outerplane bipartite graphs, which include various families of molecular graphs. Firstly, we present an algorithm for a binary coding of perfect matchings of these graphs. Further, 2- connected outerplane bipartite graphs with isomorphic resonance graphs are considered. In particular, it is shown that if two 2- connected outerplane bipartite graphs are evenly homeomorphic, then its resonance graphs are isomorphic. Moreover, we prove that for any 2-connected outerplane bipartite graph G there exists a catacondensed even ring systems H such that the resonance graphs of G and H are isomorphic. We conclude with the characterization of 2-connected outerplane bipartite graphs whose resonance graphs are daisy cubes.
{"title":"Resonance Graphs and a Binary Coding of Perfect Matchings of Outerplane Bipartite Graphs","authors":"S. Brezovnik, Niko Tratnik, Petra Žigert Pleteršek","doi":"10.46793/match.90-2.453b","DOIUrl":"https://doi.org/10.46793/match.90-2.453b","url":null,"abstract":"The aim of this paper is to investigate resonance graphs of 2- connected outerplane bipartite graphs, which include various families of molecular graphs. Firstly, we present an algorithm for a binary coding of perfect matchings of these graphs. Further, 2- connected outerplane bipartite graphs with isomorphic resonance graphs are considered. In particular, it is shown that if two 2- connected outerplane bipartite graphs are evenly homeomorphic, then its resonance graphs are isomorphic. Moreover, we prove that for any 2-connected outerplane bipartite graph G there exists a catacondensed even ring systems H such that the resonance graphs of G and H are isomorphic. We conclude with the characterization of 2-connected outerplane bipartite graphs whose resonance graphs are daisy cubes.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"9 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78042618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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